A thin strip 10 c m long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 N m - 1 (see figure). The assembly is kept in a uniform magnetic field of 0.1 T . If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N . If the mass of the strip is 50 grams, its resistance 10 Ω and air drag negligible, N will be close to:

Question

A thin strip 10 c m long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 N m - 1 (see figure). The assembly is kept in a uniform magnetic field of 0.1 T . If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N . If the mass of the strip is 50 grams, its resistance 10 Ω and air drag negligible, N will be close to:, 1000, 5000, 10000, 50000

MARKS App · Accepted Answer

Equation of motion for slider: - m d 2 x d t 2 = k x + i l B m d 2 x d t 2 + k x + B l v R l B = 0 ⇒ m d 2 x d t 2 + B 2 l 2 R . d x d t + k x = 0 Comparing with m d 2 x d t 2 + b . d x d t + k x = 0 m = m ; b = B 2 l 2 R ; k = k We know: A = A 0 e - b 2 m × t = A 0 e - B 2 l 2 2 m R × t For amplitude to be A 0 / e , A 0 e - B 2 l 2 2 m R × t = A e ⇒ B 2 l 2 2 m R × t = 1 t = 2 m R B 2 l 2 = 10,000 s e c Time period = 2 π m k = 2 s Number of oscillations = 10,000 2 = 5,000

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